Mixed number: Whole numbers with a fraction beside it; a whole and a part.
Improper fraction:A fraction in which the numerator is higher than the denominator; a fraction more than a whole.
Denominator: The denominator is the bottom that is the number of a common fraction; the divisor.
Numerator: The numerator is the top number that is the amount of parts of the denominator; the dividend.
Vinculum: The line between the numerator and denominator.
LCD/LCM: Lowest, Common, Denominator and Lowest, Common, Multiple.
Reciprocal: A fraction with its numerator and denominator switched places for certain problems
Chapter 9.4-9.5: Adding and subtracting fractions
When adding fractions with the same denominators (bottom numbers) all you have to do is add the two numerators together (top numbers). Give this a go: ------------------------------- working:
When subtracting fractions you have to do basically the same thing except you have to of course subtract the numeators. -----------------------------------working:
Fractions with different denominators:
When adding or subtracting fractions with different denominators you have to find the LCD (Lowest Common Denominator) or the LCM (Lowest Common Mulitple).
So basically to find the LCD you have to divide the numerator and denominator of the fractions until the denominators are the same, then you can add or subtract them together like the problems above. If the fractions aren't divisable then you will have to multiply the fractions until the denominators are the same to get the LCD or the LCM so you can then do the steps above. Try to find the LCD for these fractions and work them out: ---,----
Now try this: ---- ----------- ------- --working:
Here you have to multiply the first fraction. You can multiply the 15 and 6 in the first fraction by 2 then add the both fractions together. The simple answer to this problem is 21 out of 30 but simplified you get 7 out of 10. If you want to do it more "advanced" you could just take away a third of the first fractions numbers and divide the second fractions numbers by 3 and add them together to get the simplified result.
Mixed fractions:
And lastly if it is there is a mixed number you can either add the whole numbers and add the fractions like above to make a mixed fraction or you can multiply the mixed numbers by the denominators, add them to numerator and then take them away giving you a improper fraction and then add them like above. Here is a problem:
-------------------------
question/s:
Working/s:
Chapter 9.6: Multiplying Fractions
Multiplying by a fraction
When multiplying a fraction you might be given a question saying either " " or "" (this specific equation equals 6). One way is to divide the number by the denominator which will give you 1 out of what ever the denominator then multiply it by whatever the numerator is. A another way is to turn the whole number into an improper fraction and then multiply the denominators and numerators.
Try these two questions:
Multipling two fractions
When multiplying two fractions you will have to multiply the denominators and numerators and then you can simplify the result if needed. If a denominator and numerator can be divided then you can do that to get the simplified result and will not have to simplify it and you will probably have an easier multiplication sum. you whould always look for divisble to always do, here are two workings to show the difference
-------------
When multiplying mixed number fractions you will have to add the whole to the fraction to make it an improper fraction and then do the same steps as above.
------------------
Chapter 9.7: Dividing fractions
Reciprocals
Reciprocals are used in pretty much every division equation with fractions. To get the reciprocal all you have to do is switch the numerator and denominator of a fraction. Symplification may be needed if it is a mixed fraction.
Dividing by a fraction
When dividing a fraction with a number you have to find the reciprocal of the number and times the two fractions together. You might have to simplify the fractions before multiplying like above.
If there is a mixed number you just simplify and keep going.
Dividing two fractions
When dividing two fractions you have to do basically the same thing and find the reciprocal with the second fraction and multiply them together.
Just like above if there is a mixed number you just simplify and keep going.
Now here are some revision questions. I would highly suggest you grab a pen and paper because some of them can be hard!
Revision Questions:
-------
Random Notes:
35 pictures in total just so you know.
Which took me a while to do... And Im glad to say... This might have been the one of the most "time consuming" of all pages, probably because of all the smaller details.
yeah... my page isn't exactly on fraction names or their definitions but you get the point... I did it anyway! (do not copy if your doing a page on fractions)
And lastly I made that logo next to the title myself using flash, mainly because I was bored.
Well, this is the end of my page and I hope you liked this page and have learned something from it.
Welcome to my page. This page covers chapter 9.4 - 9.7 which are the mathematical operations involving fractions.
Table of Contents
Mixed number: Whole numbers with a fraction beside it; a whole and a part.
Improper fraction:A fraction in which the numerator is higher than the denominator; a fraction more than a whole.
Denominator: The denominator is the bottom that is the number of a common fraction; the divisor.
Numerator: The numerator is the top number that is the amount of parts of the denominator; the dividend.
Vinculum: The line between the numerator and denominator.
LCD/LCM: Lowest, Common, Denominator and Lowest, Common, Multiple.
Reciprocal: A fraction with its numerator and denominator switched places for certain problems
Chapter 9.4-9.5: Adding and subtracting fractions
When adding fractions with the same denominators (bottom numbers) all you have to do is add the two numerators together (top numbers). Give this a go:-------------
When subtracting fractions you have to do basically the same thing except you have to of course subtract the numeators.
--------------
Fractions with different denominators:
When adding or subtracting fractions with different denominators you have to find the LCD (Lowest Common Denominator) or the LCM (Lowest Common Mulitple).
So basically to find the LCD you have to divide the numerator and denominator of the fractions until the denominators are the same, then you can add or subtract them together like the problems above. If the fractions aren't divisable then you will have to multiply the fractions until the denominators are the same to get the LCD or the LCM so you can then do the steps above. Try to find the LCD for these fractions and work them out:
Now try this:
---- -------
Here you have to multiply the first fraction. You can multiply the 15 and 6 in the first fraction by 2 then add the both fractions together. The simple answer to this problem is 21 out of 30 but simplified you get 7 out of 10. If you want to do it more "advanced" you could just take away a third of the first fractions numbers and divide the second fractions numbers by 3 and add them together to get the simplified result.
Mixed fractions:
And lastly if it is there is a mixed number you can either add the whole numbers and add the fractions like above to make a mixed fraction or you can multiply the mixed numbers by the denominators, add them to numerator and then take them away giving you a improper fraction and then add them like above. Here is a problem:
Chapter 9.6: Multiplying Fractions
Multiplying by a fraction
When multiplying a fraction you might be given a question saying either "Try these two questions:
Multipling two fractions
When multiplying two fractions you will have to multiply the denominators and numerators and then you can simplify the result if needed. If a denominator and numerator can be divided then you can do that to get the simplified result and will not have to simplify it and you will probably have an easier multiplication sum. you whould always look for divisble to always do, here are two workings to show the differenceWhen multiplying mixed number fractions you will have to add the whole to the fraction to make it an improper fraction and then do the same steps as above.
Chapter 9.7: Dividing fractions
Reciprocals
Reciprocals are used in pretty much every division equation with fractions. To get the reciprocal all you have to do is switch the numerator and denominator of a fraction. Symplification may be needed if it is a mixed fraction.Dividing by a fraction
When dividing a fraction with a number you have to find the reciprocal of the number and times the two fractions together. You might have to simplify the fractions before multiplying like above.If there is a mixed number you just simplify and keep going.
Dividing two fractions
When dividing two fractions you have to do basically the same thing and find the reciprocal with the second fraction and multiply them together.Just like above if there is a mixed number you just simplify and keep going.
Now here are some revision questions. I would highly suggest you grab a pen and paper because some of them can be hard!
Revision Questions:
Random Notes:
35 pictures in total just so you know.
Which took me a while to do... And Im glad to say... This might have been the one of the most "time consuming" of all pages, probably because of all the smaller details.
yeah... my page isn't exactly on fraction names or their definitions but you get the point... I did it anyway! (do not copy if your doing a page on fractions)
And lastly I made that logo next to the title myself using flash, mainly because I was bored.
Well, this is the end of my page and I hope you liked this page and have learned something from it.
And if you want to know about the basics of fractions please see this page:
http://mullaunamathsrevision.wikispaces.com/Fractions-+Steph